The double-peaked emission profile has been identified by tomographic reconstruction from the signals of the tangentially viewing visible-light imaging system on EAST. In the upper-single-null discharge with neon seeding, two light emission peaks are located near the X-point and in the high-field-side (HFS) scrape-off layer (SOL) on the poloidal cross-section while the outer divertor target is still attached. The double-peaked emission phenomenon has not been reported for other tokamaks. In particular, the existence of the emission peak near the X-point under the attached condition is unexpected because it is usually an indication of X-point multifaceted asymmetric radiation from the edge under the detached condition. Therefore, it is of fundamental importance for the divertor physics to make clear the mechanism of the double-peaked emission phenomenon. The computational simulations with SOLPS-ITER and DIVIMP are performed in this work. The simulated results show the contribution of W impurity to the double-peaked emission profile is negligible with the upper tungsten divertor. Considering the existence of a lower carbon divertor in EAST, the influence of the possible deposition of the carbon on the upper divertor is further investigated. The simulating CIII (465 nm) and CII (514 nm) emissions, which make a significant contribution to the visible-light emission in channel B (blue) and G (green), respectively, are found to be similar tothe experimental results. The emission peak near the X-point is related to the carbon deposited on the dome, while that in the HFS SOL is contributed by the carbon on the inner baffle. The ionization source of the carbon impurity and the net force pointing to the X-point are analyzed to understand the concentration of the carbon impurity near the X-point, which in turn causes the emission peak.